maxima

Unfortunately, I have been having difficulties with getting $$latex$$ rendering inside code blocks. When using wxmaxima, the output from each line formats beautifully in latex, but when transferred to this blog the pretty format disappears. Hopefully I can resolve this for future posts…

I’ve recently been looking at the tools I have at my disposal for symbolic math and graphing. Disappointingly, I came up with a rather sparse list. My biggest want is to be able to solve equations symbolically (rather than numerically) and to quickly plot the result of symbolic functions. Currently, I tend to do all of the former manually (not a bad thing) and the latter with excel.

A side note; recently I’ve been finding excel absolutely indaquate to the kind of workflow and tasks that I want to be doing. I think this can be summarized by the following:

• Lack of data strcture
• Weak function library
• Constant need for ‘work-arounds’ for data manipulations
• Normalizing data? Either do it manually or set up some complicated pivot-table + reference helper tables. A great way to turn one data set into three!
• Combining lists? Do it manually.
• I could go on…

At university I used matlab + maple in my engineering degree. Both have the functionality that I’m after, but not for the price and the hassle of licensing software.

I dabbled for a very short while with Sage, but found it weirdly difficult. I’ll certainly revisit it again later, I’m not really sure how to explain my aversion to it.

So I landed on learning some Maxima. Maxima has very old, deep roots. Originated in the ’60s, open sourced in 1998, and still being actively developed. Definitely ticks the boxes for me.

A simple example that I wanted try was to plot some pressure/quantity curves for underground ventilation. The below was generated in html by wxmaxima. I really like interactively building a workbook, with inline images, in wxmaxima. This is a nice, quick, workflow that encourages trial and error.

When we’re using maxima, lines begining with (%in) are input lines, and (%on) are output lines, where n is the line number. We can use either of these references later in the code.

(%i1)	_p: R*q^2;
(%o1)	R*q^2
(%i2)	pr_n : _p, R=[0.01, 0.02, 0.03, 0.04];
(%o2)	[0.01*q^2,0.02*q^2,0.03*q^2,0.04*q^2]

(%i3)	wxplot2d(pr_n, [q, 0, 60],
[xlabel, "Quantity (m^3/s)"],
[ylabel, "Pressure (pa)"]
);

Line 1 creates an expression with the two symbols R and q. This is the equation p=R*q^2. The second line of input creates an array of expressions, substituting in R=0.01, 0.02…etc. We collect this into the variable pr_n. We could write this as

pr_n : [pr1, pr2, pr3, pr4] : _p, R=[0.01, 0.02, 0.03, 0.04]

if we wanted to keep a reference to each of the individual expressions.

The third line of input plots each of the expressions in terms of q over the range 0 to 60. It also sets labels for the two axes.

Nice one.

I’m quite happy with how that looks. In three simple lines of code we’ve done quite a bit. Next post I’ll have a look at a process for plotting a fan curve on to the same graph (or maybe a couple of fan curves). This will include sourcing data from a .csv file, plotting the discrete data and fitting a curve. A cursory glance at the curve fitting routines that maxima has indicates that the curve fitting should be more accurate than excel for my twin 45kW contra rotating CC1004. faeredia

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